# Library conventions¶

The nodedge library uses a set of standard conventions for the way that different types of standard information used by the library.

## LTI system representation¶

Linear time invariant (LTI) systems are represented in nodedge in state space, transfer function, or frequency response data (FRD) form. Most functions in the toolbox will operate on any of these data types and functions for converting between compatible types is provided.

### State space systems¶

\[\begin{split}\frac{dx}{dt} &= A x + B u \\
y &= C x + D u\end{split}\]

where u is the input, y is the output, and x is the state.

### Transfer functions¶

\[G(s) = \frac{\text{num}(s)}{\text{den}(s)}
= \frac{a_0 s^m + a_1 s^{m-1} + \cdots + a_m}
{b_0 s^n + b_1 s^{n-1} + \cdots + b_n},\]

where n is generally greater than or equal to m (for a proper transfer function).